A multiplex histopathological (H&E, IHC) slide has the potential advantage of simultaneously identifying multiple biomarkers in one tissue section as opposed to single biomarker labeling in multiple slides. Therefore, multiplex IHC slides are often used for simultaneous assessment of multiple biomarkers in cancerous tissue. Typically, a tissue slide is stained by the multiplex assay. The stained slide is then imaged using a CCD color camera mounted on a microscope or a scanner to capture the three-channel RGB color image. The acquired RGB color image is a mixture of the underlying co-localized biomarker expressions. Equivalently, the slide can be imaged using a fluorescent multispectral microscope where the captured image is a multi-channel image with each channel corresponding to a different spectral filter image capture.
For example, cancerous tissue tumors often contain infiltrates of immune cells, which may prevent the development of tumors or favor the outgrowth of tumors. In this scenario, multiple biomarkers are used to target different types of immune cells and the population distribution of each type of them is used to study the clinical outcome of the patients. In multiplex staining of cancerous tissue slides, the biomarkers of the immune cells are stained by different chromogenic dyes. In order to conduct detection and classification of the cells, stain/color unmixing of the IHC digital image is performed to generate images that reflect the individual constituent stains for each biomarker and to obtain the proportion of each stain from three-channel color pixel values of the cellular structure in the captured image. This step is a prerequisite for any follow up IHC image analysis algorithms to detect cells of different biomarker types and quantify the stain concentration
In the current literature, several techniques have been proposed to decompose each pixel of the RGB image into a collection of constituent stains and the fractions of the contributions from each of them. Ruifrok et al. developed an unmixing method called color deconvolution to unmix an RGB image, with up to three stains, in the converted optical density space. In this traditional deconvolution approach (i.e., Ruifrok's paper), shown in FIG. 1B, a linear equation yi=Axi is solved at each and every pixel i, to estimate xi where yi is the optical density transformed value of the observed RGB color value and xi denotes the vector of underlying stain proportions As xi only depends on yi and the reference vector A, solution at each pixel is independent of the solution at any other pixel in the image and thus can be solved for independent of other pixels. See Ruifrok, A C. and Johnston, D. A, Quantification of Histochemical Staining by Color Deconvolution, Anal. Quant. Cytol. Histol. 23, 291-299 (2001).
However, in multispectral unmixing or RGB unmixing, for example, where a tissue sample has been stained with multiple fluorescent stains or chromogen stains, there is a potential for imprecise knowledge of the spectral signature of the reference colors of individual stains and the inherent measurement noise in the camera capture, and Ruifrok's color deconvolution methodology may not adequately separate the unmixing components. Further, Ruifrok's method independently estimates the individual dye contributions at each pixel. Thus, Ruifrok's methodology may generate unmixed images having what appears as “holes and cracks” in the appearance of cellular structures in the unmixed images, which are biologically known to be spatially homogeneous and smooth varying. Often, these “holes and cracks” are due to the imprecise mathematical model of the physical process of image formation and noise in the imaging chain that affects the unmixed results.
Another unmixing method by Rabinovich et al. is known in the art, and it differs from Ruifrok's method in that it solves for the stain reference vectors, in addition to solving for the stain contributions at each pixel. See Rabinovich, Andrew, et al., Quantitative Spectral Decomposition for Stained Tissue Analysis, Proceedings of the University of California San Diego Research Expo (2005) p. 1-13. However, in terms of unmixing itself, Rabinovich's method is similar to Ruifrok's in that it unmixes each pixel independently Thus, like with Ruifrok's method, the tissue structural continuity is lost in the unmixed images and undesired noise or other artifacts may appear in the unmixed image results.